Spectral graph analysis of modularity and assortativity

Title

Spectral graph analysis of modularity and assortativity

 Author

Van Mieghem, P.F.A.
Ge, X.
Schumm, P.
Trajanovski, S.
Wang, H.

Faculty

Electrical Engineering, Mathematics and Computer Science

 Department

Telecommunications

 Date

2010-11-16

 Abstract

Expressions and bounds for Newman’s modularity are presented. These results reveal conditions for or properties of the maximum modularity of a network. The influence of the spectrum of the modularity matrix on the maximum modularity is discussed. The second part of the paper investigates how the maximum modularity, the number of clusters, and the hop count of the shortest paths vary when the assortativity of the graph is changed via degree-preserving rewiring. Via simulations, we show that the maximum modularity increases, the number of clusters decreases, and the average hop count and the effective graph resistance increase with increasing assortativity.

 To reference this document use:

http://resolver.tudelft.nl/uuid:7a767b6d-d235-460f-aec2-2c3013634da9

 DOI

https://doi.org/10.1103/PhysRevE.82.056113

 Publisher

American Physical Society

 ISSN

1539-3755

 Source

http://pre.aps.org/abstract/PRE/v82/i5/e056113

 Source

Physical Review E, 82 (5), 2010

 Part of collection

Institutional Repository

 Document type

journal article

 Rights

(c) 2010 The Author(s)
American Physical Society
Files
PDF vanMieghem_2010.pdf 1.09 MB
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